A displacement-based finite element formulation for the analysis of laminated composite plates

This paper presents the nodally integrated plate element (NIPE) formulation for the analysis of laminated composite plates based on the first-order shear deformation theory. The nodally integrated approach aims at providing smoothed derivative quantities by constructing nodal strain-displacement operators. Within this framework a new family of elements for plates with general monoclinic layers is developed: the strain-displacement operators are derived via nodal integration for linear triangles and quadrilateral elements. The degrees of freedom are only the primitive variables: displacements and rotations at the nodes. The NIPEs are locking-free elements, exhibit little sensitivity to geometric distortions and can be readily implemented into existing finite element codes. The efficiency of the proposed variational formulation is proved whereas effectiveness and convergence of the proposed finite elements are confirmed through several numerical applications. Finally, numerical results are compared with the corresponding analytical solutions as well as to other finite-element solutions.